A fast algorithm for learning a ranking function from large-scale data sets

We consider the problem of learning the ranking function that maximizes a generalization of the Wilcoxon-Mann-Whitney statistic on the training data. Relying on an $\epsilon$-accurate approximation for the error-function, we reduce the computational complexity of each iteration of a conjugate gradient algorithm for learning ranking functions from O(m2) to O(m2), where m is the number of training samples. Experiments on public benchmarks for ordinal regression and collaborative filtering indicate that the proposed algorithm is as accurate as the best available methods in terms of ranking accuracy, when the algorithms are trained on the same data. However, since it is several orders of magnitude faster than the current state-of-the-art approaches, it is able to leverage much larger training datasets.